Likelihood based observability analysis and confidence intervals for predictions of dynamic models

Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as well as their nonlinear impact on the model responses hamper the determination of confidence regions for parameter estimates. At the same time, classical approaches translating the uncertainty of the parameters into confidence intervals for model predictions are hardly feasible. In this article it is shown that a so-called prediction profile likelihood yields reliable confidence intervals for model predictions, despite arbitrarily complex and high-dimensional shapes of the confidence regions for the estimated parameters. Prediction confidence intervals of the dynamic states allow a data-based observability analysis. The approach renders the issue of sampling a high-dimensional parameter space into evaluating one-dimensional prediction spaces. The method is also applicable if there are non-identifiable parameters yielding to some insufficiently specified model predictions that can be interpreted as non-observability. Moreover, a validation profile likelihood is introduced that should be applied when noisy validation experiments are to be interpreted. The properties and applicability of the prediction and validation profile likelihood approaches are demonstrated by two examples, a small and instructive ODE model describing two consecutive reactions, and a realistic ODE model for the MAP kinase signal transduction pathway. The presented general approach constitutes a concept for observability analysis and for generating reliable confidence intervals of model predictions, not only, but especially suitable for mathematical models of biological systems

Effective dynamics of disordered quantum systems

We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective coupling agents and associated rates which encode the specific statistical properties of the Hamiltonian's eigenvectors and eigenvalues, respectively. Spectral disorder and isotropically disordered eigenvector distributions are considered as paradigmatic test cases.Comment: 20 page

Changing Identity: Retiring from Unemployment

Using data from the German Socio-Economic Panel from 1984-2009, we follow persons from their working life into their retirement years and find that, on average, employed people maintain their life satisfaction upon retirement, while long-term unemployed people report a substantial increase in their life satisfaction when they retire. These results are robust to controlling for changes in other life circumstances and suggest that retiring is associated with a switch in the relevant social norms that causes an increase in identity utility for the formerly unemployed. This is supportive of the idea that, by including identity in the utility function, results from the empirical life satisfaction literature can be reconciled with the economic theory of individual utility.life satisfaction, retirement, unemployment, identity, social norm

Does tax simplification yield more equity and efficiency? An empirical analysis for Germany

This paper investigates the impact of tax simplification on various indicators of the efficiency of the tax system and on the distribution of income. The analysis is based on a simulation model (FiFoSiM) using German income tax and household survey microdata. We model tax simplification as the abolition of a set of deductions from the tax base included in the German income tax system. We find that this form of tax base simplification leads to a reduction in the use of professional tax advice, a more equitable income distribution and an increase in tax revenue. If these measures are combined with a reduction of income tax rates to preserve revenue neutrality, the effects depend on the type of rate schedule adjustment. The combination with a flat rate tax implies redistribution in favour of very high incomes, and an overall increase in income inequality. Efficiency effects in terms of changes in marginal tax rates and labor supply effects are mixed. The combination with a rate schedule adjustment which preserves the directly progressive rate schedule yields a tax reform which reduces the inequality of after tax incomes. We conclude that tax simplification may improve the efficiency of the tax system without increasing inequality of after tax income. --Income distribution,polarisation,tax simplification,flat tax

Is a Flat Tax politically feasible in a grown-up Welfare State?

The introduction of a flat tax is supposed to have several advantages. Administration and compliance costs are reduced, as well as incentives for tax evasion. Furthermore, positive employment and growth effects are expected. Despite these advantages, a flat rate tax is not very popular in most Western European countries. The most important objection against a flat tax states that a flat rate tax would be inequitable and unfair. The present paper uses a simulation model based on a unique database of German micro data to provide empirical evidence for the analysis of the equity and efficiency effects as indicators for the political feasibility of flat rate tax reforms. Our analysis shows that the selection of the schedule and tax base parameters are crucial for the effects of flat tax reforms in terms of equity and efficiency. A flat rate tax with a higher basic allowance and a higher single rate has less harmful distributional effects than a flat rate tax with low basic allowance and tax rate. Nevertheless, the scenario with the lowest parameter values for basic allowance and tax rate is the only alternative that leads to positive labour supply and significantly positive welfare effects. Both labour supply and static welfare e¤ects, however, are quite small. Although we have derived our results for the case of Germany, we do think that similar patterns would be observed in other countries of Western Europe. If this proves to be correct, it will be hard for flat tax reforms to invade the grown-up welfare states of "Old Europe". --Flat Tax reform,equity,efficiency,distribution,welfare

Automatic Stabilizers, Economic Crisis and Income Distribution in Europe

This paper investigates to what extent the tax and transfer systems in Europe protect households at different income levels against losses in current income caused by economic downturns like the present financial crisis. We use a multi country micro simulation model to analyse how shocks on market income and employment are mitigated by taxes and transfers. We find that the aggregate redistributive effect of the tax and transfer systems increases in response to the shocks. But the extent to which households are protected differs across income levels and countries. In particular, there is little stabilization of disposable income for low income groups in Eastern and Southern European countries.automatic stabilization, crisis, inequality, redistribution